Much time in process mining projects is spent on nding and understanding data sources and extracting the event data needed. As a result, only a fraction of time is spent actually applying techniques to discover, control and predict the business process. Moreover, there is a lack of techniques to display relationships on top of databases without the need to express a complex query to get the required information. In this paper, a novel modeling technique that works on top of databases is presented. This technique is able to show a multigraph representing activities inferred from database events, connected with edges that are annotated with frequency and performance information. The representation may be the entry point to apply advanced process mining techniques that work on classic event logs, as the model provides a simple way to retrieve a classic event log from a speci ed piece of model. Comparison with similar techniques and an empirical evaluation are provided.
This paper introduces StarStar models, a novel way to enable Process Mining on
database events that o ers the best qualities of competing techniques,
providing a model representation without any e ort required to the user, and o ering
drill-down possibilities to get a classic event log. The technique takes into
account relational databases, that are often used to support information systems.
Events in databases could be logged in several ways, including redo logs and
in-table versioning. To retrieve an event log suitable for process mining analysis,
a case notion (a view on the data) should be chosen, choosing speci c tables and
columns to be included in the event log. In order to obtain the view, a SQL query
needs to be expressed and this requires a deep knowledge of the process.
Moreover, this could also take to some performance issues (requiring joins between
several tables). Some approaches have been introduced in literature in order to
make the retrieval of event logs from databases easier: OpenSLEX meta-models
[
StarStar models take as input an event log in a database context. In order to provide a de nition of this concept (Def. 1), let UO be the universe of objects, UOC be the universe of object classes, UA be the universe of activities, Uattr be the universe of attribute names, Uval be the universe of attribute values. It is possible to de ne a function class : UO ! UOC that associates each object to the corresponding object class.
De nition 1 (Event log in a database context) An event log in a database context is a tuple LD = (E; act; attr; EO; ) where E UE is a set of events, act 2 E ! UA maps events onto activities, attr 2 E ! (Uattr 6! Uval) maps events onto a partial function assigning values to some attributes, EO E UO relates events to sets of object references, E E de nes a total order on events.
An example attribute of an event e is the timestamp attr(e)(time) which refer
to the time the event happened. To project an event log in a database context to
a classic event log, a case notion (a set CD P(E) n ; such that Sx2CD x = E)
needs to be chosen, so events that should belong to the same case can be grouped.
The projection function is trivial to de ne, and further details could be found
in [
The E2O graph is obtained directly from the data without any transformation. The remaining steps in the construction of a StarStar model are the construction of the E2E multigraph and of the A2A multigraph. Let g : UO ! P(UE ), g(o) = fe 2 UE j (e; o) 2 EOg be a function that for each object returns the set of events 1 that are related to the object, w : UO ! R, w(o) = jg(o)j+1 be the weight of the object de ned as the inverse of the cardinality of the set of related events to the given object plus 1, ]k : UO ! UE , ]k(o) = e such that e 2 g(o) ^ jfe0 2 g(o) j e0 egj = k for 1 k jg(o)j be a function that in the totally ordered set g(o) returns the k-th element.
De nition 3 (E2E multigraph) Let LD = (E; act; attr; EO; ) be an event log in a database context. Let FE = f(o; i) j o 2 O ^ 2 i jg(o)jg such that for fE 2 FE the following attributes are de ned: oEbj(fE ) 2 O is the object associated to the edge, iEn(fE ) 2 E is the input event associated to the edge, oEut(fE ) 2 E is the output event associated to the edge, weight(fE ) 2 R+ associates each edge to a positive real number expressing E its weight, pEerf(fE ) 2 R+ [ f0g associates each edge to a non-negative real number expressing its performance. For fE = (o; i) 2 FE : oEbj(fE ) = o, iEn(fE ) = ]i 1(o), oEut(fE ) = ]i(o), wEeight(fE ) = w(o), pEerf(fE ) = attr( out(fE ))(time) attr( in(fE ))(time). The event to event multigraph (E2E) can be introduced having events as nodes and associating each couple of events (e1; e2) 2 E E to the following set of edges: RE (e1; e2) = fE 2 FE j iEn(fE ) = e1 ^ oEut(fE ) = e2 .
A representation of the E2E multigraph draws as many edges between a couple of
events (e1; e2) 2 E E as the number of elements contained in the set RE (e1; e2).
To each edge fE 2 RE (e1; e2), a label could be associated in the representation
taking as example the weight wEeight(fE ) or the performance pEerf(fE ).
De nition 4 (A2A multigraph) Let LD = (E; act; attr; EO; ) be an event
log in a database context. Let FA = f(c; (a1; a2)) j c 2 UOC ^ (a1; a2) 2
UA UAg such that for fA 2 FA the following attributes are de ned: cAlass(fA) 2
UOC is the class associated to the edge, iAn(fA) 2 UA is the source activity
associated to the edge, oAut(fA) 2 UA is the target activity associated to the
edge, cAount(fA) 2 N associates each edge to a natural number expressing the
number of occurrences, wAeight(fA) 2 R+ associates each edge to a positive real
number expressing its weight, pAerf(fA) 2 R+ [ f0g associates each edge to a
non-negative real number expressing its performance. Let AE : FA ! P(FE ) be
a function such that for fa 2 FA: AE(fA) = f fE 2 FE j class( oEbj(fE )) =
cAlass(fA) ^ act( iEn(fE )) = iAn(fA) ^ act( oEut(fE )) = oAut(fA) g. Then
for fA = (c; (a1; a2)) 2 FA: cAlass(fA) = c, iAn(fA) = a1, oAut(fA) = a2,
cAount(fA) = jAE(fA)j, wAeight(fA) = PfE2AE(fA) wEeight(fE ), pAerf(fA) =
PfE2AEA(fA) pEerf(fE) . The activities multigraph (A2A) can be introduced having
count(fA)
activities as nodes and associating each couple of activities (a1; a2) 2 A A to the
following set of edges: RA(a1; a2) = oAut(fA) = a2
fA 2 FA j iAn(fA) = a1 ^
A representation of the A2A multigraph (that is the visual element of a StarStar
model) draws as many edges between a couple of activities (a1; a2) 2 A A as
the number of elements contained in the set RA(a1; a2). To each edge fA 2
RA(a1; a2), a label could be associated in the representation taking as example
the number of occurrences cAount(fA), the weight wAeight(fA) or the
performance pAerf(fA). Since by construction the edges in this graph can be associated
to elements in the E2E graph (through the AE function), the possibility to drill
down to a classic event log (choosing a case notion) is maintained. Indeed, it is
possible to de ne a projection function from an event log in database context to a
classic event log (more insights on the di erences could be found in [
In order to evaluate StarStar models, a ProM plug-in has been realized that is
able to take as input a representation of the events happening at database level, is
able to calculate the StarStar model starting from the data and to show it to the
end user using the mxGraph library. The supported input data types include
XOC logs [
This paper introduces StarStar models, providing a way to reduce ETL e orts on databases in order to enable process mining projects. StarStar models provide a multigraph visualization of the relationships between activities happening in a database, and the possibility to drill down. By selecting any case notion interactively we get a classic event log that can be analyzed using existing process mining techniques. Each step in the construction of a StarStar model has linear complexity and can be done on graph databases. A plug-in has been implemented on the ProM framework that can import the data, build the StarStar model, provide a visualization of the activities multigraph, and provide projection functions.